At the extragalactic scale, we seek to understand the relationship between stellar
density and gas density that was put forward by
[1]} and [2]}), and crystallized in a relationship between the observable surface density
of SFR, \(\Sigma _{SFR}\) , and the surface density of gas, \(\Sigma {_{gas}}\) ,
as: \(\Sigma _{SFR} = A~\Sigma {_{gas}^N}\)  by [3]} and [4]}.
However, this relation is not scale-invariant, the power-law indexes depend on the
size scales of the objects, as pointed out using the diffuse cloud tracer CO 1–0 and radio continuum luminosity ().
These relationships may behave differently if one considers
only dense gas tracers, as was suggested for extragalactic
environment ([5]}, ).
The linear relationship manifests in the
extragalactic environments ([6]}) and in the Milky Way environments ([7]}), but significant gaps remain between
extragalactic and galactic star formation laws ([8]}).
Nevertheless, the linear relationship between dense gas and SFR shows
real scatter in excess of observational uncertainties ([9]}),
so additional factors are at work beyond a simple “more dense gas gives
more star formation” model.
